code: def block_homomorphism(group, blocks):
      """
      Return the homomorphism induced by the action of the permutation
      group ``group`` on the block system ``blocks``. The latter should be
      of the same form as returned by the ``minimal_block`` method for
      permutation groups, namely a list of length ``group.degree`` where
      the i-th entry is a representative of the block i belongs to.
  
      """
      from sympy.combinatorics import Permutation
      from sympy.combinatorics.named_groups import SymmetricGroup
  
      n = len(blocks)
  
      # number the blocks; m is the total number,
      # b is such that b[i] is the number of the block i belongs to,
      # p is the list of length m such that p[i] is the representative
      # of the i-th block
      m = 0
      p = []
      b = [None] * n
      for i in range(n):
          if blocks[i] == i:
              p.append(i)
              b[i] = m
              m += 1
      for i in range(n):
          b[i] = b[blocks[i]]
  
      codomain = SymmetricGroup(m)
      # the list corresponding to the identity permutation in codomain
      identity = range(m)
      images = {
          g: Permutation([b[p[i] ^ g] for i in identity])
          for g in group.generators
      }
      H = GroupHomomorphism(group, codomain, images)
      return H
  
imports: import itertools
  from sympy.combinatorics.fp_groups import FpGroup, FpSubgroup, simplify_presentation
  from sympy.combinatorics.free_groups import FreeGroup
  from sympy.combinatorics.perm_groups import PermutationGroup
  from sympy.core.intfunc import igcd
  from sympy.ntheory.factor_ import totient
  from sympy.core.singleton import S
label_desc: Use image node_id 4 for calling a global function with example usage: block_homomorphism(group, blocks) and returns: H